Maths-
General
Easy
Question
The expressions x2 + bx + 10 and (x - 3)2 + c, where b and c are constants, are equivalent. What is the value of
b + c?
- 7
- 4
- 3
- -5
The correct answer is: -5
We are given that the 2 equations are equivalent. Therefore we simplify the 2 equations and compare the 2 to find our solution.
Step-by-step solution:-
Equation 1 = x2 + bx + 10
Here, a1 = 1, b1 = b & c1 = 10
Equation 2 = (x - 3)2 + c
= x2 - 6x + 9 + c __________________________ [(a+b)2 = a2 + 2ab + b2)]
Here, a2 = 1, b2 = -6 & c2 = 9 + c
We know that the 2 equations are equivalent
Therefore- a1 = a2, b1 = b2 & c1 = c2
Solving for b - b1 = b2
i.e. b = -6 _________________________ (Equation i)
Solving for c - c1 = c2
i.e. 10 = 9 + c
10 - 9 = c
i.e. c = 1 ____________________________. (equation ii)
To find- b + c = -6 + 1 _________________________ (From equations i & ii)
= -5
Final Answer:-
Option D i.e. -5 is the correct Option.
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